Equation 677 Database

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Magma 39ff25f9c769…

magma 39ff25f9c769
Size
321
Isomorphism class hash
39ff25f9c7694562203808d30fd48fb86a949d43f905ed85fa2c2f992d700c11
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 320) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-01 22:37:38
Display reorder
300,214,35,109,142,120,215,33,110,143,121,213,34,108,141,122,31,210,112,138,123,211,32,113,139,124,30,212,111,140,125,115,205,26,133,126,116,206,24,134,127,114,204,25,132,128,208,118,29,136,129,209,119,27,137,130,207,117,28,135,131,304,301,307,309,295,195,294,293,292,298,196,299,297,296,290,197,291,288,289,194,279,278,276,277,283,192,282,281,280,193,287,286,285,284,258,259,201,256,257,263,262,202,260,261,254,255,203,252,253,270,271,200,268,269,275,274,198,273,272,266,267,199,264,265,319,317,320,318,248,95,249,178,5,250,93,251,179,3,246,94,247,177,4,91,240,241,174,0,242,92,243,175,2,90,244,245,176,1,231,230,86,169,11,232,233,84,170,9,229,228,85,168,10,237,236,89,172,7,239,238,87,173,8,235,234,88,171,6,313,314,311,312,226,82,191,106,165,227,83,189,107,167,225,81,190,105,163,78,222,187,102,157,223,79,188,103,159,80,224,186,104,161,182,217,73,97,146,180,218,74,98,148,181,216,72,96,145,220,185,76,100,152,221,183,77,101,154,219,184,75,99,150,303,305,302,310,164,12,43,61,50,166,13,44,62,48,162,14,42,60,49,15,156,46,64,53,158,16,47,65,51,17,160,45,63,52,41,147,18,67,56,39,149,19,68,54,40,144,20,66,55,153,37,21,70,59,155,38,22,71,57,151,36,23,69,58,308,316,315,306 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 321 = 1 + 5*64, from a common submagma at infinity. C(E, M, k, B) adjoins a submagma M (m elements) of a model E to every group of a transversal design TD(k, g), g = |E| - m, so that every enlarged group is a copy of E and all of them share M; every block carries B, a model of order k in which x*x = x. Two elements of M multiply in M; an element of M or of group i with one of group i, in group i's copy of E; elements of different groups, in their block. It satisfies Equation 677 whenever E and B do. This magma is C(E, M, 5, B) with E = magma#73fd82887325b6d09523ca7385118fdff4d39fe9410b39daf9f2816ebeaae0b3, M = {60} in E, B = magma#e549b5f8492c9b6b5ad530e3aa4f39c6e23d08645ebd1b36a3c2de2a5a23bac5. Labels: 0..m-1 are M, in increasing order of their labels in E; m + g*i + c (i < k, c < g) is point c of group i, which plays the c-th element of E outside M, in increasing order. A block's point in group i plays element i of B. TD(5, 64): MacNeish's product over GF(64); GF(64) = F_2[x]/(x^6 + x + 1); GF(p^r) = F_p[x]/(f) labels c_0 + c_1 x + ... as c_0 + c_1 p + ..., and point c of a group is the c-th element of the product in lexicographic order. Block (a, b), a and b in the product, meets group i in the point whose coordinate in each field is a + s_i b, s_i the element of that field labelled i, or b when the field has exactly i elements. Equation 255: satisfied. Idempotent elements: 21.

last edited by qawbecrdtey at 2026-10-01 22:37:38 · history